Data volume managed by information systems represented by a cloud-based system continues to increase. Research for applying these data is advanced, while at the same time, it is regarded as important how to keep privacy of data in the information systems. To realize this, research for applying data, maintaining privacy of the data exists. For example, in Patent Literature 1 and Non-patent Literature 1, an encryption method of verifying whether a server holds identical data with data held by a client in a server-client model or not (searching identical data) is disclosed.